I'm fairly certain she does plan on breast-feeding.
Many disordered mothers who try to edge out fathers will claim, "I have to breasfeed every X hours, I can't let the baby out of my sight for more than a couple hours!" Well, most courts realize that's not the case. After all, millions of working mothers go back to work within 2-3 months. If they can do it, so can she. (Side point, beware of her using the baby as an excuse not to go back to work!) Besides, she could express her milk and send it with the baby/toddler at exchanges.
She may insist to supervise your visits. Beware of that tactic. You need your own parenting time away from her suspicions and control.
Another point, she will try to claim the baby is too small for overnights. Another claim without any medical foundation. Yes, courts do generally set schedules for new fathers to shorter visits and maybe not entire weekends, but they are frequent, every 2-3 days or so. Don't be emotionally pressured to cave to the claim you can't properly care for your child. By the time a child is 3 years old, if not sooner, then standard schedules kick in.
For example, she has hinted that she does not feel comfortable with me being alone with the baby because she's worried I might be a child abuser. This thought has no basis in reality.
Sadly, this is an all-too-common tactic used against targeted fathers. Courts deal with such claims all the time.
I faced repeated allegations I was dangerous to my child. My ex went to as many agencies as she could to paint me as a dangerous abuser. After the first few times they reacted less and less. It would be good to establish now that she is prepping herself to make allegations. I recorded once I discerned my marriage was about to implode. Over ten years later I still have them, though I guess I really don't need them any more after all this time. But back then it really felt touch and go. Without them I would have felt defenseless with no way to document that I wasn't the one threatnening, I wasn't the one misbehaving. No court, children's agency, police, sheriffs, hospitals cared one bit that my parental contact was blocked, to them it was another day at work. In one stretch it was 3 months and when we finally got a hearing in court and the magistrate confirmed from her that she had blocked all contact for 3 months, by then our son was 4 years old, he said, "I'll fix that." All he did was assign me and schedule again with alternate weekends and a 3 hour visit in between. No lectures to her (consequences), no make up time for me (credit). Sadly, court isn't about being fair so you have to (politely) stand up for yourself at the right times and right places.